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Full text of "Mathematical And Physical Papers - Iii"

62 ON THE EFFECT OF THE INTERNAL FRICTION OF FLUIDS communicate a second memoir in continuation of the first. This memoir, so far as I can find out, has never appeared. Should the existence of such forces in the superficial film of a liquid be made out, the results deduced from the theory of internal friction will be modified in a manner analogous to that in which the results deduced from the common principles of hydrostatics are modified by capillary attraction. It may be remarked that we have nothing to do with forces of this kind in considering the motion of pendulums in air, or even in considering the oscillations of a sphere in water, except as regards the very minute fraction of the whole effect which relates to the resistance experienced by the suspending wire in the immediate neighbourhood of the free surface. It may readily be seen that the effect of a set of forces in the superficial film of a liquid offering a peculiar resistance to the relative motion of the particles would be, to make the resistance of a gas to a descending globule agree still more closely with the result obtained by regarding the globule as solid, while the resistance experienced by an ascending bubble would be materially increased, and made to approach to that which would belong to a solid sphere of the same size without mass, or more strictly, with a mass only equal to that of the gas forming the bubble. Possibly the determination of the velocity of ascent of very small bubbles may turn out to be a good mode of measuring the amount of friction in the superficial film of a liquid, if it be true that forces of this kind have any existence. But any investigation relating to such a subject would at present be premature. 45. Let us now attempt to determine the uniform motion of a fluid about an infinite cylinder. Employing the notation of Section III., and reducing the problem to one of steady motion as in Art. 39, we obtain the same equations of condition (116), (117), as in the case of the sphere. Assuming % = sin 6 F(r), and substituting in the equation obtained from (69) by transforming to polar coordinates and leaving out the terms which involve d/dt, we get The integral of this equation may readily be obtained by multiplying the last term of the operating factor by (1 + £)2, integrating the transformed equation, and then making 8 vanish. It is F(r) = Ar-l + £r+Crlogr+I)r* .........(130)